Dissipation Concept Research Articles

Mini-Workshop: Mathematics of Dissipation – Dynamics, Data and Control

Dissipation of energy — as well as its sibling the increase of entropy — are fundamental facts inherent to any physical system. The concept of dissipativity has been extended to a more general system theoretic setting via port-Hamiltonian systems and this framework is a driver of innovations in many of areas of science and technology. The particular strength of the approach lies in the modularity of modeling, the strong geometric, analytic and algebraic properties and the very good approximation properties.

Data-Driven Dissipativity Analysis: Application of the Matrix S-Lemma

The concept of dissipativity, as introduced by Jan Willems, is one of the cornerstones of systems and control theory. Typically, dissipativity properties are verified by resorting to a mathematical model of the system under consideration. This article aims to assess dissipativity using computing storage functions for linear systems directly from measured data. As our main contributions, we provide conditions under which dissipativity can be ascertained from a finite collection of noisy data samples. Three different noise models are considered that can capture a variety of situations, including the cases where the data samples are noise-free, the energy of the noise is bounded, or the individual noise samples are bounded. All conditions are phrased in terms of data-based linear matrix inequalities, which can be readily solved using existing software packages.

Robust distributed economic model predictive control based on differential dissipativity

AbstractIn this article, a robust distributed economic model predictive control (DEMPC) approach is developed for plant‐wide chemical processes. The proposed approach achieves arbitrary feasible setpoints that may vary frequently, attenuates the plant‐wide effects of unknown disturbances and minimizes a plant‐wide economic cost. In this approach, a plant‐wide process is represented as a network of process units and each process unit is controlled by an individual controller which shares a plant‐wide optimization economic objective and stability conditions through the network. To ensure the convergence of process variables to arbitrary setpoints, a contraction condition is developed for the DEMPC, based on the contraction theory. To deal with the effects of interactions among process units, the concept of dissipativity is adopted. Using sum‐separable control contraction metrics, a reference‐independent robust stability condition is developed to ensure the plant‐wide disturbance effects (under interactions among process units) to be attenuated in terms of differential ℒ2 gain and represented by a plant‐wide differential dissipativity condition, which is converted into the differential dissipativity conditions that individual controllers need to satisfy. This approach facilitates the optimization of plant‐wide economic costs with global constraints in a distributed way, allowing efficient implementation of alternating direction method of multipliers (ADMM). The proposed approach is illustrated using a reactor‐separator process.

Design of Resilient Reliable Dissipativity Control for Systems With Actuator Faults and Probabilistic Time-Delay Signals via Sampled-Data Approach

The issue of resilient reliable dissipativity performance index for systems including actuator faults and probabilistic time-delay signals via sampled-data control approach is investigated. Specifically, random variables governed by the Bernoulli distribution are examined in detail for the random time-delay signals. By using the Lyapunov–Krasovskii functionals together with the Wirtinger double integral inequality approach and reciprocally convex combination technique, which reflects complete information on the certain random sampling; as a result, a new set of sufficient criterion is launched to ensure that the proposed closed-loop system is strictly ${(\mathbb {Q},\mathbb {S},\mathbb {R})}$ - ${\gamma }$ -dissipative. The proposed criterion for dissipativity-based resilient reliable controller is expressed in the form of linear matrix inequalities. The major contributions of this paper is ${(\mathbb {Q},\mathbb {S},\mathbb {R})}$ - ${\gamma }$ -dissipativity concept can be adopted to analyze more dynamical performances simultaneously, such as ${\mathcal {H}_\infty }$ , passivity, mixed ${\mathcal {H}_\infty }$ , and passivity performance for the proposed system model by choosing the weighting matrices ${(\mathbb {Q},\mathbb {S},\mathbb {R})}$ . Finally, an interesting simulation example is demonstrated to showing the applicability and effectiveness of the theoretical results together with proposed control law by taking the experimental values of the high-incidence research model and rotary servo system.

Where does energy go when it's “Gone”? Promoting understanding of energy dissipation

The principle of energy conservation cannot be fully accepted or applied in most real-world contexts without an understanding and acceptance of the idea of dissipation: when the perceptible changes in the system have stopped, the energy that was present in the beginning is still present in the system and its environment, even if it is no longer detectable. This idea is challenging for learners of all ages and presents a serious obstacle to understanding. Results from Focus on Energy, an innovative elementary-school energy curriculum, show that fourth- and fifth-grade students can engage productively with the idea of dissipation, leading to a model of energy that includes dissipation. The curriculum does not explicitly include dissipation as a learning target, but it includes early and frequent exposure to dissipative phenomena, a meaningful conceptual framework, and appropriate representational tools. These resources offer opportunities to reason about dissipation and incorporate it into the students' developing energy model. In an open-response assessment, 23% of Focus on Energy students spontaneously included dissipation in their tracking of energy in a wind-up toy, compared to 3% for students who received standard energy instruction. Adult teachers experience similar difficulties with the concept of dissipation, and results from professional development workshops show that the same curricular approach is effective with these adult learners. We suggest that if young children and adult teachers can begin to reconcile energy conservation and energy dissipation, then similar instructional approaches could enable high school and college students to engage productively with dissipation ideas.

Teaching Fluid Mechanics and Thermodynamics Simultaneously through Pipeline Flow Experiments

Entropy and entropy generation are abstract and illusive concepts for undergraduate students. In general, students find it difficult to visualize entropy generation in real (irreversible) processes, especially at a mechanistic level. Fluid mechanics laboratory can assist students in making the concepts of entropy and entropy generation more tangible. In flow of real fluids, dissipation of mechanical energy takes place due to friction in fluids. The dissipation of mechanical energy in pipeline flow is reflected in loss of pressure of fluid. The degradation of high quality mechanical energy into low quality frictional heat (internal energy) is simultaneously reflected in the generation of entropy. Thus, experiments involving measurements of pressure gradient as a function of flow rate in pipes offer an opportunity for students to visualize and quantify entropy generation in real processes. In this article, the background in fluid mechanics and thermodynamics relevant to the concepts of mechanical energy dissipation, entropy and entropy generation are reviewed briefly. The link between entropy generation and mechanical energy dissipation in pipe flow experiments is demonstrated both theoretically and experimentally. The rate of entropy generation in pipeline flow of Newtonian fluids is quantified through measurements of pressure gradient as a function of flow rate for a number of test fluids. The factors affecting the rate of entropy generation in pipeline flows are discussed.

Pilot Scale Extraction of Orthosiphon stamineus Raw Material as Rosmarinic Acid Extract

A scale-up protocol for rosmarinic acid extraction from Orthosiphon stamineus was developed using the concept of constant power dissipation for a similar kinetic profile. Rosmarinic acid is the bioactive compound in the herb and therefore, large scale extraction for that compound is important for commercial application. The first-order kinetic equation which was established in the preparative scale extraction was used to describe the extraction of rosmarinic acid from the herb. The agitation speed of the pilot large-scale extractor (451 rpm) was determined based on the constant power dissipation to meet the minimal required speed, namely just-suspended speed (Njs), 450.84 ± 0.88 rpm. The experimental data was fitted well to the proposed kinetic equation with a high correlation coefficient, R2 0.88, and a low root mean square error, RMSE 3.85. This indicates the good performance of the scale-up approach based on the dynamic criterion. Therefore, the use of constant power dissipation to obtain a similar kinetic profile could be applied for phytochemical extraction from herbal plants.

Dissipativity of positive switched systems using multiple linear supply rates

In this paper, we are devoted to investigating dissipativity for a class of positive switched systems by exploiting multiple linear copositive storage functions and multiple linear supply rates. A novel concept of dissipativity is presented, which depicts the overall dissipativity property of positive switched systems without the requirement of the classic dissipativity property of each positive subsystem. A sufficient condition ensuring dissipativity for positive switched systems is given under a designed switching signal. Meanwhile, L1 gain and stability are also get based on dissipativity. Dissipativity and positivity are shown to be maintained under positive feedback interconnection, and a small-gain property is also given. All presented conditions are formulated as a linear programming problem. Two examples are provided to illustrate the effectiveness of the main results.

Study on Influence of Diversified Parameters of Vehicle and Track on Wheel Hollow Wear

Wheel hollow wear of high‐speed train is one of the main damage types for the wheel. By optimizing the vehicle and track parameters and matching the wheel‐rail profile, the hollow wear of wheel can be reduced. In order to study the sensitivity of vehicle and track parameters to the wheel hollow wear, the sensitivity of suspension parameters and the track parameters of the CRH2Ctype high‐speed train wheel on the hollow wear of the wheel was studied by the parameter sensitivity analysis method. The concept of the cumulative wear power dissipation was put forward. The distribution characteristics of the wheel hollow wear under the different wheel/rail treads matching were forecasted. The results show that the damping of antihunting motion damper of the vehicle is the most sensitive to the maximum cumulative wear power dissipation of the wheel, followed by the longitudinal stiffness of tumbler journal box node, lateral stiffness of air‐spring suspension, vertical damping of primary suspension, vertical stiffness of track, and vertical damping of track. According to the analysis from the combination of sensitive parameters, the cumulative wear power dissipation is unevenly distributed in the lateral direction of the wheel tread and has the obvious peak area, which is basically the same as the actual wear distribution location in the field. The matching of the LMA wheel tread and the CN60N rail tread is a good choice to slow down the hollow wear and reduce the wheel wear rate. And the wheel reprofiling should be timely carried out, otherwise the wear rate would increase and the hollow wear would become more serious.

A Dissipative Systems Theory for FDTD With Application to Stability Analysis and Subgridding

This paper establishes a far-reaching connection between the Finite-Difference Time-Domain method (FDTD) and the theory of dissipative systems. The FDTD equations for a rectangular region are written as a dynamical system having the magnetic and electric fields on the boundary as inputs and outputs. Suitable expressions for the energy stored in the region and the energy absorbed from the boundaries are introduced, and used to show that the FDTD system is dissipative under a generalized Courant-Friedrichs-Lewy condition. Based on the concept of dissipation, a powerful theoretical framework to investigate the stability of FDTD methods is devised. The new method makes FDTD stability proofs simpler, more intuitive, and modular. Stability conditions can indeed be given on the individual components (e.g. boundary conditions, meshes, embedded models) instead of the whole coupled setup. As an example of application, we derive a new subgridding method with material traverse, arbitrary grid refinement, and guaranteed stability. The method is easy to implement and has a straightforward stability proof. Numerical results confirm its stability, low reflections, and ability to handle material traverse.

Mean-square dissipativity of numerical methods for a class of resource-competition models with fractional Brownian motion

ABSTRACTThe concept of dissipativity in dynamical systems generalizes the idea of a Lyapunov stability. In this paper the dissipativity is used to designate that the system possesses a bounded absorbing set. Specifically, this paper studies mean-square dissipativity of two numerical methods for a class of resource-competition models with fractional Brownian motion (fBm). Some conditions under which the underlying systems are mean-square dissipative are established. It is shown that the mean-square dissipativity is preserved by the split-step θ-method (SSθ) under some constraints, while the split-step backward Euler method (SSBE) could inherit mean-square dissipativity without any restriction on stepsize. The results of this study indicate that the split-step backward Euler method (SSBE) outperforms the split-step θ-method (SSθ) in terms of mean-square dissipativity. Finally, an example is given to illustrate the effectiveness of the results.

Comparative study of different combustion models for turbulent gas flames

Several popular turbulent combustion models have been tested in a computational study of three experimentally well-documented non-swirling and swirling jet flames. Different combinations of turbulence, combustion and reaction mechanisms models were considered. It is shown that the eddy- dissipation concept (EDC) and the probability-density function (PDF) of flamelet combustion models with detailed kinetics mechanisms provide the best results for all flames examined. For some cases, a combination of RANS turbulence models and less costly combustion approaches (Hybrid or EDC with 4 reactions) also gives acceptable results.

Incremental (Q,S,R)-dissipativity and incremental stability for switched nonlinear systems

This paper investigates incremental (Q,S,R)-dissipativity and incremental stability for switched nonlinear systems whose subsystems are not required to be incrementally (Q,S,R)-dissipative. Firstly, an incremental (Q,S,R)-dissipativity concept is proposed for switched nonlinear systems. We show that an incrementally (Q,S,R)-dissipative switched nonlinear system is incrementally stable. Secondly, the sufficient conditions for switched nonlinear systems to be incrementally (Q,S,R)-dissipative are given by the design of state-dependent switching laws. Finally, this incremental (Q,S,R)-dissipativity property is shown to be invariant under compatible feedback interconnection by the design of a composite state-dependent switching law. The numeral examples are presented to illustrate the effectiveness of the proposed approach.

Entransy analysis for irreversible gas power cycles with temperature-dependent specific heat

Because of the energy needs of the world and the problem of global warming, developing more efficient power cycles has become an obligation. In this paper, concepts of entransy dissipation, entropy generation, power output, exergy output, energy, exergy efficiencies for irreversible spark injection, compression injection engines and irreversible gas turbine cycle are applied for their analyses. Optimum values were determined using compression and pressure ratios. A model was developed for the specific heat of the working fluid that depends on temperature to obtain more explicit results. The numerical results are presented and optimum values are defined for the cycles. Finally, suggestions regarding the design and operating conditions for the cycles are presented.

The Application of Entransy Dissipation Theory on the Performance Analysis of an Irreversible Atkinson Cycle

Several techniques on the Second Law of Thermodynamics have been used in the past for the analysis of Air standard Cycles. The terms used for these techniques include irreversibility analysis, entropy generation minimization, exergy analysis and thermodynamic efficiency. Entransy is a recently developed concept reflecting the heat transfer potential, rather than the ability to convert heat to work. This paper extends this concept to optimize thermodynamic processes of an irreversible Atkinson cycle. The entransy balance equation of thermodynamic processes is introduced, with which the concept of entransy dissipation is developed. For the irreversible Atkinson cycle where the working fluid is heated by the streams with prescribed inlet temperatures and specific capacity flow rates, it is found that the maximum entransy dissipation leads to the maximum output work, which is the maximum principle of entransy dissipation in thermodynamic processes. At the same time, it is found that minimum entropy generation alone could not describe change of the output work for the Atkinson cycle. The operation parameters are optimized for evaluating the maximum output work of Atkinson cycle by incorporating maximum entransy dissipation and minimum entropy generation when both, entransy dissipation and entropy generation, are induced by dumping the used streams into the environment is considered.

Control of plant-wide systems using dynamic supply rates

This paper presents a framework for analysis of plant-wide processes from a network perspective. Using the concept of dissipativity, the conditions for plant-wide input–output stability and performance are developed, based on the dissipativity of individual subsystems and the topology of the network of the plant-wide process. Dynamic supply rates, expressed as quadratic differential forms, are proposed not only to render dissipativity based analysis less conservative but also allow the dynamic plant-wide performance criteria to be specified in terms of desired closed loop supply rates. The links between the plant-wide supply rate, finite L2 gain in an extended input–output space and weighted H∞ norm are explored in this paper. These results lay a foundation for a supply rate-centric approach to plant-wide distributed control.

Distributed control of plant-wide chemical processes with uncertain time-delays

This paper presents a distributed control approach for large and complex process plants with uncertain time-delays such as variable transport delays in the physical flow between process units and communication delays in the distributed controller network. In this framework, a plant-wide process is modeled as a network of linear time-invariant process units and is controlled by a network of distributed controllers. Using such a network representation, the effects of delay uncertainties on plant-wide stability and performance are studied based on the concept of dissipativity. A controller design procedure that takes into account the delay uncertainties is also formulated, which allows each distributed controller to be designed individually. This leads to an autonomous and distributed control strategy that can efficiently handle the effects of time-delays in both the process and controller networks.

Mechanism and Dynamic Behavior of a Novel Hydraulic Force Pulse Generator

Based on the concept of hydraulic damper energy dissipation, a passive Hydraulic Force Pulse Generator (HFPG) is presented. The design comprises a conical poppet valve inside a cylindrical hole without any seat. By virtue of aperture and orifice throttling, HFPG dissipates the kinetic energy of a rapidly moving object and cushions it to a halt to produce desired acceleration pulse. Prompt and easy adjustment can be achieved to the damping force by changing the size of the orifice set on cylinder. A mathematical model of the cushion process is developed by way of analyzing the internal fluid dynamic phenomenon of HFPG. And numerical simulation results of the model has exhibited the following features of HFPG: high-efficiency of energy dissipation; easy-regulation of acceleration waveform and being suitable in conditions with large momentum change, especially to be used as the negative pulse generator of dual-wave shock testing machines which can simulate the shock environment of underwater explosion.

Dissipative mechanism of a semilinear higher order parabolic equation in [formula omitted

It is known that the concept of dissipativeness is fundamental for understanding the asymptotic behavior of solutions to evolutionary problems. In this paper we investigate the dissipative mechanism for some semilinear fourth-order parabolic equations in the spaces of Bessel potentials and discuss some weak conditions that lead to the existence of a compact global attractor. While for second-order reaction–diffusion equations the dissipativeness mechanism has already been satisfactorily understood (see Arrieta et al. (2004), doi:10.1142/S0218202504003234 [7]), for higher order problems in unbounded domains it has not yet been fully developed. As shown throughout the paper, one of the main differences from the case of reaction–diffusion equations stems from the lack of a maximum principle. Thus we have to rely here on suitable energy estimates for the solutions. As in the case of second-order reaction–diffusion equations, we show here that both linear and nonlinear terms have to collaborate in order to produce dissipativeness. Thus, the dissipative mechanisms in second-order and fourth-order equations are similar, although the lack of a maximum principle makes the proofs more difficult and the results not as complete.Finally, we make essential use of the sharp results of Cholewa and Rodriguez-Bernal (2012), doi:10.1016/j.na.2011.08.022 [12], on linear fourth-order equations with a very large class of linear potentials.

Dissipativity Analysis of Linear State/Input Delay Systems

This paper discusses dissipativity problem for system of linear state/input delay equations. Motivated by dissipativity theory of control systems, we choose a new quadratic supply rate. Using the concept of dissipativity, necessary and sufficient conditions for the linear state/input delay systems to be dissipative and exponentially dissipative are derived. The connection of dissipativity with stability is also considered. Finally, passivity and finite gain are explored, correspondingly. The positive‐real and bounded‐real lemmas are derived.